In this problem, we explore the effect on the standard deviation of multiplying

Question

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 16, 15, 9, 15, 9. Use the defining formula, the computation formula, or a calculator to compute s. () s = Multiply each data value by 7 to obtain the new data set 112, 105, 63, 105, 63. Compute s. () s = Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c? Multiplying each data value by the same constant c results in the standard deviation being |c| times as large. Multiplying each data value by the same constant c results in the standard deviation remaining the same. Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. Multiplying each data value by the same constant c results in the standard deviation increasing by c units. You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.1 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? Yes No Given 1 mile = 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) s = km One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80. If a data set has mean 70 and standard deviation 5, is 80 a suspect

Explanation / Answer

a. Step 1: Find the mean. (X¯)

In this example:Xbar =12.8.

Step 2: Create the following table

Step 3: Find the sum of numbers in the last column to get.

(xiX¯)2=48.8

Step 4: Calculate using the above formula.

=sqrt((xiX¯)2/n1)=sqrt(48.8/51)3.492

b. Step 1: Find the mean. (X¯)

In this example: X¯=89.6.

Step 2: Create the following table.

Step 3: Find the sum of numbers in the last column to get.

(xiX¯)2=2391.2

Step 4: Calculate using the above formula.

=sqrt((xiX¯)2/n1)=sqrt(2391.2/51)24.4499

data data-mean (data - mean)2 16 3.2 10.24 15 2.2 4.84 9 -3.8 14.44 15 2.2 4.84 9 -3.8 14.44

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